Members of the IRA are not currently involved in training or other activities in the Republic, the Taoiseach, Mr Ahern, has said, following a series of security briefings from top Garda officers.
"Paramilitary activity - training, targeting and those things in the Republic - that is not an issue at the moment," Mr Ahern said on Today FM's Sunday Supplement programme.
Earlier the Minister for Justice, Equality and Law Reform, Mr McDowell, said the IRA had "stood down" its Dublin Brigade in recent months.
"A number of its members were shot in the ankles for diverting money from the movement. After that, it took over direct management of the 'funding' of its criminal operations through its Belfast Brigade," Mr McDowell said.
However, the IRA had brought a halt to its criminal actions in the Republic in the run-up to the last round of negotiations, which ended in failure early this month.
"That [criminal activity] has now stopped as far as I know in the run-up to this particular set of negotiations. It is very significant. It shows they can do without that method of fundraising.
"I have no evidence they have engaged in that kind of major robbery in the Republic from the summer onwards," the Minister told the Sunday Business Post.
"There have been a number of incidents involving a number of IRA members, none of it qualifies as major crime and I am not in a position to answer the question about whether the small stuff is authorised or not."
However, he said the IRA was involved in knee-cappings, punishment beatings, and smuggling activities in Northern Ireland, along with truck robberies.
"Near the border, fuel tankers passing up particular roads have to pay a £400 tax to members of the IRA," Mr McDowell said.
Meanwhile, the Taoiseach has conceded that the disagreement between Sinn Féin and the Democratic Unionist Party over the photographing of IRA weapons decommissioning would not be resolved quickly.
Asked if any progress had been made, the Taoiseach said: "No, there is none whatsoever and I don't see any movement quite frankly in the short term, if at all. "Unfortunately now we are going to drift out over the Christmas period. We will keep at it," Mr Ahern said, adding that the Government would "stay in touch" with the British government.
"I don't accept that we have to leave this until the other side of the summer and the local elections and possibly the general election. The regrettable thing is that we had achieved so much."
An early December agreement would have prompted complete IRA decommissioning by the end of this month, and speedy progress on other matters. "So many of these things were on the table," he said.
"We were a long way there, but unfortunately it happens on the North, you get stuck on an issue," Mr Ahern said, adding that the Government had demanded a complete end to IRA criminality.
"I think certainly paramilitary activity as we define paramilitary activity, this has been a very quiet year. That has been our security briefings. We want to broaden that out to see the end of illegal activity in its broadest sense.
He and Mr McDowell had "been determined to get to an understanding" on illegal IRA activity, he said.